Drag each step and justification to the correct location in the table. Each step and justification can be used more than once, but not all steps and justifications will be used.

Order each step and justification needed to solve the equation below.
[tex]\[ \frac{2}{3} y + 15 = 9 \][/tex]

\begin{tabular}{|c|c|}
\hline
Steps & Justifications \\
\hline
\frac{2}{3} y + 15 = 9 & Given \\
\hline
\frac{2}{3} y + 15 - 15 = 9 - 15 & Subtraction property of equality \\
\hline
\frac{2}{3} y = -6 & Simplification \\
\hline
\frac{2}{3} y \cdot \frac{3}{2} = -6 \cdot \frac{3}{2} & Multiplication property of equality \\
\hline
y = -9 & Simplification \\
\hline
\end{tabular}



Answer :

Sure, let's complete the table with the correct steps and justifications needed to solve the given equation [tex]\(\frac{2}{3} y + 15 = 9\)[/tex].

We will follow the already provided steps and justifications:

1. Start with the given equation: [tex]\(\frac{2}{3} y + 15 = 9\)[/tex]
2. Subtract 15 from both sides: [tex]\(\frac{2}{3} y + 15 - 15 = 9 - 15\)[/tex]
3. Simplify the equation: [tex]\(\frac{2}{3} y = -6\)[/tex]
4. Multiply both sides by the reciprocal of [tex]\(\frac{2}{3}\)[/tex], which is [tex]\(\frac{3}{2}\)[/tex]: [tex]\(\frac{2}{3} y \cdot \frac{3}{2} = -6 \cdot \frac{3}{2}\)[/tex]
5. Simplify: [tex]\(y = -9\)[/tex]

These steps and justifications can be placed in the table as follows:

\begin{tabular}{|c|c|}
\hline
Steps & Justifications \\
\hline
[tex]\(\frac{2}{3} y + 15 = 9\)[/tex] & Given \\
\hline
[tex]\(\frac{2}{3} y + 15 - 15 = 9 - 15\)[/tex] & Subtraction property of equality \\
\hline
[tex]\(\frac{2}{3} y = -6\)[/tex] & Simplification \\
\hline
[tex]\(\frac{2}{3} y \cdot \frac{3}{2} = -6 \cdot \frac{3}{2}\)[/tex] & Multiplication property of equality \\
\hline
[tex]\(y = -9\)[/tex] & Simplification \\
\hline
\end{tabular}

Let's put each part in context to ensure the solution path aligns correctly:

1. Step: [tex]\(\frac{2}{3} y + 15 = 9\)[/tex] Justification: Given
2. Step: [tex]\(\frac{2}{3} y + 15 - 15 = 9 - 15\)[/tex] Justification: Subtraction property of equality
3. Step: [tex]\(\frac{2}{3} y = -6\)[/tex] Justification: Simplification
4. Step: [tex]\(\frac{2}{3} y \cdot \frac{3}{2} = -6 \cdot \frac{3}{2}\)[/tex] Justification: Multiplication property of equality
5. Step: [tex]\(y = -9\)[/tex] Justification: Simplification

These are the correct steps and justifications needed to solve the equation [tex]\(\frac{2}{3} y + 15 = 9\)[/tex].